Is it useful to eliminate the less relevant filters from a trained CNN?
NOTE: All the observations and results are from the paper The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks.

To answer your questions one by one:


Yes there are ways to determine which filters have more impact on the output. Its a very naive way but works very good in practice. Filters with small weights impact output less (according to empirical evidence), which basically means neurons whose weights lie in the switching region i.e ~$0$ in ReLu and ~$-1$ to $1$ (say) have less impact on final output.
Yes, just eliminating these lower weight filters eliminate the unnecessary noise and indecisiveness introduced by these filters and suprisingly makes the model perform better (observed empirically).
The concept a relatively old paradigm but has been a new twist by the simplicity of the method of elimination of unnecessary weights in the aforementioned paper and thus winning it the best paper award in ICLR 2019. 


TL;DR: Eliminating unnecessary weights makes the model perform better than the original model.

Also here is the TensorFlow code.